solution_3 - 30 January, 2006 Michael F. Brown CHEMISTRY...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 30 January, 2006 Michael F. Brown CHEMISTRY 481 (Biophysical Chemistry) Problem Set 03 To be turned in by: Monday, 06 February Worked examples for this course are dealt with primarily in the Discussion Section; whereas new concepts are introduced in the Lectures. You can get help with the homework problems in the Discussion Sections (12:30—13:20 Tues, Koeffler 216; and 13:00—13:50 Wed, Koeffler 216). The problem sets will be graded P+, P, or F and will be used to increase or decrease borderline grades. On all computational problems be sure to use SI units, and indicate your answer to the proper number of significant figures. For maximum credit show clearly how you obtained your answer, i.e. what numbers were combined to yield the final result. Background reading: Atkins & de Paula, Chapter 12 Examples and exercises related to the homework (optional): Back of Chapter Exercises: 12.6, 12.7, 12.9, 12.12 Back of Chapter Problems: 12.2, 12.15 Problem 1. Consider a particle in a 1-dimensional box for which the wave function is: 1p (x) = 3 sin (Ex) " L L a) Show that the above wave function is an eigenfunction of the Hamiltonian for the region between the walls where V = 0: b) Using the result of part (a), what is the energy of the nth level? Problem 2. A biochemist is studying the process of vision and is interested in the spectroscopic properties of retinal. The structure of all-trans-retinal is indicated below: \ \ \ \ \0 Let us apply the free electron model to retinal and assume that the length of the conjugated system is L = 1.3 nm. Calculate the wavelength A of the light that is absorbed by retinal. Problem 3. A biophysical chemist is applying the free electron model to the electronic properties of chlorophyll. a) Write the Schrodinger equation for a particle in a square well of length L: b) Calculate the expectation values of the momentum f) and the square of the momentum 132 for a particle in the state n = 1: -1- Problem 4. A biochemist is interested in determining the amount of secondary structure (hydrogen bonding) in a newly discovered protein from human immunodeficiency virus (HIV). One can assume a quantum mechanical harmonic oscillator model for the N—H stretching vibrations of the peptide bonds. For the harmonic oscillator the energy levels are given by: E =(v+ %)“hu) v (D=I\’k/pl a) Write the Schrodinger equation in terms of the reduced mass it, being sure to define all symbols. where: b) Calculate the frequency of the infrared radiation absorbed by the N—H bonds in ,B-sheet regions of a protein in wavenumbers. Assume that the force constant is k = 650 N m—l. c) Calculate the frequency of the infrared radiation absorbed by the N—H bonds in non- hydrogen bonded regions of a protein in wavenumbers. Assume that the force constant is k = 690 N m—l. d) Explain the influence of hydrogen bonding on the N—H stretching frequencies of proteins in simple physical terms. 01 —30-06 chem48 1\06\prob\003\mw 100 ’5 a“) 79 544w W 7% (x!) 75 “1 672nf«ma»q c/‘Wé/a/M'b‘wvan a/eravfim we new! 710 S/MW 060d: gay/2 : El) ’49,, 6/”r’jénfunafi‘yn rub” '\_, (/“A/d/“W (-3) €1,7enV0‘i/JQ éénW/j) 0? W6 #WW-véfflm‘a/r‘ dféfau‘or‘ ig/I'VQ? (IV; 4_-;—279+V =_;,-242 H _ 9-07 6‘07 Z??- 7h2/é/9re we need ’47 7’ 7‘65 277/ Mun/1.4714. df V4093: JV»? _(2—)'§-j_7_7_ : m7} dz - L (L L) 1% - -(ga V2417: 25.7 5,»; 7??” L (1— (L— (1— 2 2 - = 1151) (Li/WW1? Lpfi/MM,_‘__,_,J I k may ’1 - -773 d; n /-/ —7 fl “7’4 37h ’99? ..__ 7* 77" 2‘ “(3%)(1) 476’ ._/'b'1 ’7 Af‘ 127/ Sig/if“) ‘p” = 061/77)4/n z; 3A,,(meg/7h/Man “KK, ./ ms/Wj E é/jor‘L/dv/JJ,€ gimp, 45m é/rfn vdw 67M7m 4/; oékufld 127 5721924427 WM 4%,)(() [AJ/‘M‘ /7‘ j (N? yr; ;§ fl/r aywr’hvjv‘m MW flaruL/mm. w;— /» 66-711 5) 7/76 @2299 fie 0/6 @re/ 2: ‘5’}??? %/:‘g eye» Vex/MG 65W 59 a/m‘nfi mm fl¢ flaw/fifemm # c720. 1752 ééwmfluofim 3%6d; k//,n¢v £7060 1" En’ynO‘) ,4; 590a») fry/’9’? (a): g m L ".3 .‘ fr 5/7 7*; m. we see ;4Mew2/e?w; nib; _E,7 = gm 1.?“ fl _Jv. :2, We 6’4u_£_,__2ix_z/o we /e ban of: @ergxhfl V, a flz‘onfla/i meme (/2~2 de/Ogfl 32¢ fl'S’ C cardaidfzil 17 ,_7__ .— é 7L? 1 ( dr/k/f in g éax ;H1L ,hv’ 1L_ 5 €9164W?a#anlhaflz/fl)_ .. _._ 3—. _ ._—‘ ‘ _ __ _ ,,,, ,~}_,1L_- _. L _ W 1 A 3/77L2" Subsf/Yafz :_ 7_ * .__w_-. 7 _Ac £5: Mfr—— __ ____-/fi\__2#f _k -_ ._:;_§ C..__,— 3 [- C _____.,, #%_A “4.5 (MW _ — gch; rww__mmwm__mvmrm_ (207‘0/2 3 (£7 (Mo x {0" Egon/0507;: 29:33: (54777 72 Z 32‘) 7" / 2 {6. 6916K magi—$7 ;:._ 4.13 7-x;alim. =— f: 39—/%/¢7H*{7é/76‘0F7 —4// M05 fefl;?Mj—— F—f—gW—(Wf—H =7er 6/6 an e [50’ d! 24/2” 7 . 1K 3. ¢ " = L {55/~<1:>(-V;1)7/§w<%)a ‘1779‘ L 57’» 13 dx L O L- Jxl 1. L a 7 =23???” 5073/25“ EL f 441 c/x LJO A I ( 1“ , 1KL - -1 r ' ‘ :—_/ 9~(fl> (1/?) ,/—sm dz t—Jo ,L L- L, L .7 ‘ +iéé7i7¢ SM (/(sfhquyfl Aw 4) -e n :Rjjzy?’_/X_ Ls/n(2l_7‘x)]/L H 7 L3 Si +77- 4 0 25327?“ , .. - ./_ a--~ A? g: <1. 02 (9,1 0)] P'W/fl. é; .* £3 ,2 £3 £3 4%ng A; -/-x 7-3.!— $137 2‘ 3’- fl I .é’ 4a 7‘4? ['7/052/QMS asks us- 7‘0 0739/7 7‘17? ham/mom} asd/éu’ar/mc/e/ 7‘0 7%6 N’H bOnJ w’braxz'ans af 4 f¢f65en aim/XV? pro/21rd f/JM 7‘54 fl/V. 51> .2772; 9696 Orly/7514‘; gear-£2 dFSCK/‘Aég 7‘56 Mddzp; V(>() :- 3Eng wheré k: vioch cmsflmf _ , X 1 dlgp/menzl from €7W;Z¢£FJUM J70 sffloh (y: 0*) use of x6 is 0/07 ; \/(><) : i k (w “)2 #énce' 7/56 agrokgkgr (ZWI'O'I') .75 I _7I52 3*) 20, = .7; 6/ .... -1 w dvefurJO/ldn (e—7’Wc/fon __4_%v+:/<>< fl, 5%, ) U) 9% 1x3- Mera K“ “’3; 5 ("NW .1. :. _._[__ g. .1. fl mN my MWthyJ/agdfl MfiM (~71 \' rag-:74 (3% ruff/djgfigddm b) 77%. fré’gaérmy 47L in/Mnda’ rag/Lidia“ AbSO/be/J by WV? berm/5 3/7 fl’S/uech (Kg/hing [5; A5 : 5”” —Ey I (2+ /7‘é)z§w —- (V+J;)7l?w = fled IQ‘Q/N‘jnfc é AE05c://a/—or I Efl—iw KCanserl/ou‘fdh 03L 7% w 2 by N advenomber 5 f. 35>) I {if = km; W 4 3‘; >3) : ’é/ar>‘/ 7 = J. t 2/7; .2: /U0v~J ;//’S 7/;Me JO Sw,ésj//'/U/¢7 7’66 mu%,764/ (/d/Ugs: 5 N ’ w __ i/ / . :3 I ' / 5‘0le J— +_./_. > v 5fl9v7?QX/03mS-I){(é \)(/4r0/ Loo; (/.ééo§x/o"*/24_ = 3’42§'X/o5—m‘/ m: kgms-a _ R - : CE-Ms’x/oy w’)(/0 cm) / N /M y : 3 O 5M-/ (bydngei-I EOMt/Qa’) emf. I}, 4. Conf, é) Ugh; flee lzswéf we Je/Iued In paw-7‘ (6‘)) A) / 1/ v : A ,2: __ an //a // :4 / (é? n7") __/____ 7‘, / / :1 9FK2,7‘/2x aims—){ x4.0/ /.oo 2 l r?\\- ‘3 /6605'x/0 77¢ch _ - «2 = 3-537X/0’m/ ’N'K’iMS _ (3,694 x /0",¢7 ’)//o:"crn ./ K m y — .>.a3~/ CM (hdh'hydrdij‘gh gang/ed) ‘ . » a /‘}‘ A z r ’ r ," ‘ ’ - (I) [3/6 N Vic é1/6, 74‘ Lb? 0 Hr é, 6W7 3’6'4/ [54500/2? Sig/4‘; 2; Sq’ehce "' “cm” - 327' W6 W2 Canal/car 0'7 (ounfi/JW/Mé’ )fi “gaze/.- I? 6" —c—c—N~C —C-’-( — ‘X l 94 ll “i' H 0 5 : O I C I a 7 _, ——l'-'...,"_. _'_. __ .._ x! - g4 N (C! C", i 0 7/7é7 é/f6d 0f Aydfojéh bandich an fee Aj’g/ f/éflmc}€s Java/(la; dry/(94999627, 53(qufifi;-log%flvm 75 a/ro (d/‘rWJ 7‘0 #1222 f/éc/‘rdhég dive, Onyenfi A/-—/,4 band 75 gfi’flggtgg/Lflgzaker Man in He: 4(aseuce 07" 4747/59“ band/(“y 5/3164? five hydrocqa‘n 7; shared [92 )Zuuéen vao dam: rdjf’héf 7597M 642/7131 Covq/en-H7 bandd —/o a Sig/e, dam. @567 wZv'J‘Vj WW ewe/fig "Nee—J 741i 5+Efdv'u; Ls /€ ...
View Full Document

This note was uploaded on 04/02/2008 for the course CHEM 481 taught by Professor Brown during the Spring '06 term at University of Arizona- Tucson.

Page1 / 9

solution_3 - 30 January, 2006 Michael F. Brown CHEMISTRY...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online